Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9177)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=-13/4

http://functions.wolfram.com/07.23.03.9177.01

Input Form

Hypergeometric2F1[-(23/4), -(13/4), 5, -z] == (1/(157941385977375 Pi z^4)) (4096 (1 + z)^(1/4) (4 (-307648 - 7191272 z - 97779187 z^2 - 1326275335 z^3 + 61825498245 z^4 - 175232800071 z^5 + 120642492831 z^6 - 19003646829 z^7 + 17784975 z^8 + 480675 z^9) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - 2 (-307648 - 7191272 z - 97779187 z^2 - 1326275335 z^3 + 61825498245 z^4 - 175232800071 z^5 + 120642492831 z^6 - 19003646829 z^7 + 17784975 z^8 + 480675 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (615296 + 13921072 z + 185189675 z^2 + 2515262750 z^3 - 48396522195 z^4 + 93994609632 z^5 - 41403741771 z^6 + 2908083750 z^7 + 69697875 z^8 + 1922700 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])]))

Standard Form

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MathML Form

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</apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]